Cool, always fun to revisit this one.
I definitely see the evil. She goes and tests people by her religion, in a test that can kill them. She does not ask if they want to take the test. These people do not come to her wishing to take the test. In fact Gangplank is begging her not to do it.
She does it anyway, fulling thinking that she's going to kill Gangplank. Which, honestly, I don't have a problem with since Gangplank is a piece of shit mass murdering sociopath. But the implication is, that doesn't matter. He could have been the sweetest guy who ever lived, but if he wasn't "in motion" she still would have tested him and potentially killed him.
That's horrifying. That is straight up religious extremism of the weirdest and worst sort. Imagine that, people coming up to you, saying you have to follow the tenets of their religion and then forcing you to take a test that you could die from without your permission. Because that's what she's doing. She just has some bullshit excuse about how it's your duty to be in motion. She's basically the villain from the Saw movies, but instead of making the torture external, it's internal and motivated by her incredibly screwed up religion.
And we may try to justify that horrifying shit by saying that "she's just trying for motion, so people can reach their full potential." But let's look at that. Motion isn't inherently good. Neither is people's potential. We see that first hand, since basically what Gangplank gets out of his little test was that he should go and become an even bigger dickbag, who kills more, and destroys more, just so he can grab power and become the best pirate ever, potentially getting a whole bunch of people killed in the process. And Illaoi knows this, and is totally ok with it. That is basically giving Jeffery Dahmer a pep talk, saying "Yeah, you raped and murdered 17 guys? Why stop there? Go big! Go rape and murder another 100! More than that! You get the gold medal for best serial killer if you kill another 121! Shoot for the stars, buddy!"
That's why she's blatantly evil.
Remember, if we're going by the old D&D alignment system. Neutral means you still prefer good, you just don't go out of your way to do anything about it. Evil is where you literally don't care about the destruction you're unleashing, about the murders you're committing. And make no mistake, she is committing murder by forcing people to undergo her test. And she clearly doesn't care about the people she just unleashed a newly motivated Gangplank on. Hell, her main motivation for fighting against the monster of the Black Mist is because she has a hangup about the undead.
Now as to Lawful. Lawful and Chaotic in D&D alignment is funny. Because it's almost (but not entirely) meaningless. There are really two things that aren't actually at all related that make up the Lawful/Chaotic alignment. One is following the laws of the country you're in. The other is following personal oaths. But the thing is, everyone follows their personal ideology, it just matters where you're arguing from. And if you define lawful as following the actual laws, that means a Lawful Good character who enters a Lawful Evil country, with rules like "it's totally cool to kill slaves" would suddenly stop being lawful if they try to mess with those rules. Which is entirely against the other concept of standing up for your moral codes. These contradictions make the Lawful/Chaotic axis pretty annoying to define, since it mostly involves what each people think are more important.
For example, take the most cited Chaotic Good character ever, Robin Hood. He steals, that's chaotic. And he gives to the poor, that's good. He's chaotic good! But he isn't. If you read the old legends, Robin is attacking the unlawful government under King John, and disrupting illegal tax collectors. That's following the old governments, pretty lawfully. Hell, he is even gathering the money for the freeing of his true ruler, King Richard the Lionhard. And of all the characters in the old legends, he's the only one who is almost unfailingly loyal about it. Even Friar Tuck had his moments of fallacy. But not Robin. Certainly this makes him the most Lawful character in the stories. And almost every character can be defined like that.
Which brings me back to Illaoi. We see her following her personal creed even if she doesn't want to, even when it could kill a lover. That is straight lawful conduct right there. She has her code, and she sticks to it, no matter the cost to her and those she's close to. That's directly taken from the second aspect of lawfulness.
And I, definitely see personal codes as the more important aspect of Lawful. Because I'm an old school gamer, and I have read the rules of places like The Drow Kingdoms, where the law is to be a chaotic murdering lunatic. And that leads to other weird nonsense questions such as "if the law says to be chaotic, then by definition everyone chaotic just became lawful." Which thoroughly breaks with the simplicity of what the alignment system was originally meant to convey.
Anyway, if you made it through all that. That's my take. Illaoi. A Lawful Evil character, who preaches a True Neutral religion. Fun stuff, interesting character. Still evil, though.